I thin it may really depend on what group of natives you are talking to. If you are in Australia, aboriginal is more often seen. Here in the US its a mixture of both Native Americans/Indians. In Central America its often more complex. Generally if you aren't trying to be offensive, its pretty clear I feel to most people
As for the slavery topic... the greatest pro slavery intellectuals of the deep south continuously argued for its expansion. Most were afraid of continued population dynamics if slave populations grew without the land to utilize them efficiently. The fact that heavy overwork had largely drained the soils of Virginia and other parts of the upper south and that slavery was migrating south/west throughout the 19th century shows that slavery would not simply have shriveled up and died, but rather moved to different regions. Democrat efforts at the time to annex Cuba, the Yucatan, additional land in Mexico often had this goal in mind for a safety valve for Slavery. Take the case of Polk for example, he expanded the US significantly into Mexico - but couldn't take more of Mexico because of Northern opposition against the spread of slavery which enraged the South. If the CSA had became independent, you know they wouldn't have been satisfied with the limited land conquest of Polk - and would have ended up annexing Cuba, the Yucatan, most of Mexico, etc. In Texas's constitution following annexation, direct mentions to the spread of slavery were made - with even a provision being slipped in, to potentially split Texas into four different states to give slavery more representation and opportunity to spread.
Slavery wasn't dying - but southern slaveholders feared the North's growing backbone against it. Northern reaction was inevitable due to poor southern politics, but slavery in the US if played all over again probably would still only choke to death on the barrel of a civil war rifle.